Question

Differentiate y =
$\sqrt{x { }^{2} } + 5$
​

Answer 1

Step-by-step explanation:

$\sf{\dfrac{dy}{dx} = \sqrt{x^2} + 5}$

We need to differentiate it.

Now, as 5 is a constant, so it is 0.

We need to differentiate $\sf{\sqrt{x^2}}$

And, $\sf{\sqrt{x^2}}$ = x, because root and square get cancelled.

What we need now :-

$\sf{\dfrac{d(x)}{dx} }$

And, dx/dx gives out result as 1.

So, the answer is 1.

A quick run through:-

There are different rules which are :-

• Constant multiplier rule
• Constant rule
• Sum or difference rule
• Product rule
• Quotient rule
• Chain rule

This question was attempted under sum or difference rule, which states :-

If $\sf{y = f(x) + g(x) - h(x)}$

So,

$\sf{\dfrac{dy}{dx} = \dfrac{d f(x)}{dx} +\dfrac{d g(x)}{dx} - \dfrac{d h(x)}{dx}}$